Question: Simplify the following expression: $p = \dfrac{t^2 + 8t - 9}{t - 1} $
Solution: First factor the polynomial in the numerator. $ t^2 + 8t - 9 = (t - 1)(t + 9) $ So we can rewrite the expression as: $p = \dfrac{(t - 1)(t + 9)}{t - 1} $ We can divide the numerator and denominator by $(t - 1)$ on condition that $t \neq 1$ Therefore $p = t + 9; t \neq 1$